Writing code to implement Runge-Kutta methods 1 and 4 for a second order nonlinear ODE

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Bear12
Bear12 2016-5-5
回答： Manali Gupta 2019-6-21
Hi, I am very stuck... I rewrote the equation to where it is written as two 1st order ODE's.
Given: y"(t)+0.05y'(t)+y^3(t)=7.5cos(t)
After re-writing I have:
y_1=y y'_1=y_2
y_2=y' y'_2=-0.05y_2-(y^3_1)+7.5cos(t)
So,
y_(1,i+1)=y_(1,i)+h*y_(2,i) y_(2,i+1)=y_(2,i)+h*(-0.05y_(2,i)-y^3_1+7.5cos(t)
Initial conditions as: y_1(0)=0 and y_2(0)=1
I need to implement these y_1 and y_2 into the Runge Kutta methods for RK1 and RK4.
Thank you!
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James Tursa
James Tursa 2016-5-5
@Jan: The usual meaning is RK1 is 1st order Runge Kutta (i.e., Euler Method), and RK4 is 4th order Runge Kutta.
James Tursa
James Tursa 2016-5-5
@Bear12: Are you intending to use MATLAB provided functions for the integration? I.e., ode45? Or are you supposed to write the RK1 and RK4 integration code yourself?

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回答（1 个）

Manali Gupta
Manali Gupta 2019-6-21
Hi,
Attached file trk.m calculates the derivatives of the variables. The RK4 algorithm to solve the set of equations is implemented in solveOde.m.
I hope this helps.

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